Five employees of the ministry of mines and petroleum were killed and 10 wounded in the bus attack, the officials said, adding that seven people were killed and more than 20 wounded in the second explosion, presstv.ir reported.
"First a magnetic bomb pasted to a minibus exploded, then a suicide bomber blew himself near the bus attack site and the third blast happened when a car was blown up by unknown militants," said Nasrat Rahimi, a spokesman of the interior ministry in Kabul.
"The death toll could rise from all the three blasts," he said.
No militant group has claimed responsibility for the attacks that came as US Marine General Joseph Dunford, the chairman of the Joint Chiefs of Staff, was meeting top US and NATO officials in Kabul.
The United States is trying to negotiate a deal that would see foreign forces pull out of Afghanistan in return for various security guarantees by Taliban militants, including a pledge that the country will not become a safe haven for terror groups.
Afghan security experts said the insurgents were increasing attacks to gain greater leverage in the peace talks.
The eighth round of talks is expected to begin this month in Qatar.